Come for the productivity, stay for the philosophy
There’s a large class of things that eventually make you more effective when you’ve studied them for a while, but which are challenging and seem like they produce no gains while being learned.
Formal logic, for instance, seems that way for a lot of people.
Many of the natural sciences have this characteristic.
Some philosophical concepts have this characteristic.
For this class of thing, I’ve always found a strategy of “Come for the productivity, stay for the philosophy” to be effective.
In my experience, if people can get real and tangible gains and improvements out of a set of ideas quickly, they’re more likely to stick around and be patient with the more abstract things.
Advanced students and practitioners in a domain often forget how expensive their field was to learn originally and how little gain there might seem to be in that field for new people, so they often neglect this.
I don’t have a longer post to write. I just think this is really important to think about from time to time and encourage you to do so. It can make teaching and learning much more effective. Give it a try, maybe, next time you’re teaching in an abstract domain.
What tangible results could the person get now so they’re more likely to stick around for abstract learnings?
This isn’t necessarily “Come for the instrumentality, stay for the epistemology” — but, maybe.
Thing that made my thinking clearer that isn’t widespread: thinking in terms of factor analysis when trying to build models.
It would be nice to collect examples on such things (e.g., studying X in the long term helped me with Y problem through concept Z). It could help people decide what to study and insipre them to keep doing it.
This might be useful in relatively young fields (e.g. information theory) , or ones where the topic itself thwarts any serious tower-building (e.g. archaeology), but in general I think this is likely to be misleading. Important problems often require substantial background to recognize as important, or even as problems.
A list of applications of sophisticated math to physics which is aimed at laymen is going to end up looking a lot like a list of applications of sophisticated math to astrophysics, even though condensed matter is an order of magnitude larger, and larger for sensible reasons. Understanding topological insulators (which could plausibly lead to, among other things, practical quantum computers) is more important than understanding fast radio bursts (which are almost certainly not alien transmissions). But a “fast radio burst” is literally just a burst of radio waves that appeared and disappeared really fast. A neutron star is a star made of neutrons. An exoplanet is a planet that’s exo. A topological insulator is … an insulator that’s topological? Well, A: no, not really, and B: now explain what topological means.
Once people can ask well-posed questions, providing further motivation is easy. It’s getting them to that point that’s hard.
Unfortunately, there are a lot of teachers out there who don’t follow this kind of practice for their students.
Many of these (or other) theory things never make you “more effective”. But you do become able to interact with them.